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The displacement of an object attached to Spring and executing Association is given by X = 2 * 10 raise to power minus 2 cos Pi M the time at which its maximum speed first occur is?
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The displacement of an object attached to Spring and executing Associa...
Analysis of the given displacement equation:
The displacement of the object attached to a Spring executing Simple Harmonic Motion (SHM) is given by the equation:
X = 2 * 10^-2 * cos(πt)
Finding the maximum speed:
The maximum speed of the object occurs when the displacement is at its maximum or minimum value. In this case, the maximum displacement is 2 * 10^-2. The velocity of the object is given by the derivative of the displacement equation:
V = -2 * 10^-2 * π * sin(πt)
To find the time at which the maximum speed first occurs, we need to find when the velocity is at its maximum. The maximum velocity occurs when sin(πt) is equal to -1 or 1. Since sin(πt) oscillates between -1 and 1, the first time the maximum velocity occurs is when sin(πt) = -1.
Calculating the time for maximum speed:
sin(πt) = -1
πt = -π/2
t = -1/2
Therefore, the time at which the maximum speed first occurs is t = -1/2 seconds.
Conclusion:
By analyzing the given displacement equation and understanding the relationship between displacement, velocity, and time in Simple Harmonic Motion, we were able to determine the time at which the maximum speed first occurs for the object attached to the Spring.
The displacement of the object attached to a Spring executing Simple Harmonic Motion (SHM) is given by the equation:
X = 2 * 10^-2 * cos(πt)
Finding the maximum speed:
The maximum speed of the object occurs when the displacement is at its maximum or minimum value. In this case, the maximum displacement is 2 * 10^-2. The velocity of the object is given by the derivative of the displacement equation:
V = -2 * 10^-2 * π * sin(πt)
To find the time at which the maximum speed first occurs, we need to find when the velocity is at its maximum. The maximum velocity occurs when sin(πt) is equal to -1 or 1. Since sin(πt) oscillates between -1 and 1, the first time the maximum velocity occurs is when sin(πt) = -1.
Calculating the time for maximum speed:
sin(πt) = -1
πt = -π/2
t = -1/2
Therefore, the time at which the maximum speed first occurs is t = -1/2 seconds.
Conclusion:
By analyzing the given displacement equation and understanding the relationship between displacement, velocity, and time in Simple Harmonic Motion, we were able to determine the time at which the maximum speed first occurs for the object attached to the Spring.
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The displacement of an object attached to Spring and executing Association is given by X = 2 * 10 raise to power minus 2 cos Pi M the time at which its maximum speed first occur is?
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The displacement of an object attached to Spring and executing Association is given by X = 2 * 10 raise to power minus 2 cos Pi M the time at which its maximum speed first occur is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The displacement of an object attached to Spring and executing Association is given by X = 2 * 10 raise to power minus 2 cos Pi M the time at which its maximum speed first occur is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The displacement of an object attached to Spring and executing Association is given by X = 2 * 10 raise to power minus 2 cos Pi M the time at which its maximum speed first occur is?.
The displacement of an object attached to Spring and executing Association is given by X = 2 * 10 raise to power minus 2 cos Pi M the time at which its maximum speed first occur is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The displacement of an object attached to Spring and executing Association is given by X = 2 * 10 raise to power minus 2 cos Pi M the time at which its maximum speed first occur is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The displacement of an object attached to Spring and executing Association is given by X = 2 * 10 raise to power minus 2 cos Pi M the time at which its maximum speed first occur is?.
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